arXiv:2610.07606v1 Announce Type: new
Abstract: This paper establishes a theoretical framework for vertical adaptive layer skipping, proving three foundational results: (i) an Expected FLOPs formula (theorem 2) giving a closed-form expression for the computational cost of arbitrary per-sample skip schedules as a function of layer-wise skip probabilities; (ii) function-space superset (theorem 10) and strict inclusion (theorem 11) theorems showing that skip-layer models are strictly contained in—yet meaningfully approximate—the full-layer function space, with an explicit separating example; and (iii) a structural duality between VALSE and Mixture-of-Experts architectures (proposition 6), positioning vertical depth-wise sparsity as the orthogonal counterpart to horizontal width-wise sparsity. Building on this theory, we propose VALSE (Vertical Adaptive Layer Skipping for Efficiency), a per-sample, non-contiguous layer skipping method: a lightweight difficulty estimator scores each input from the first few layers, and per-layer gates selectively skip redundant layers—including arbitrary middle layers while retaining deeper ones—so that only the necessary depth is activated for each input, whose feasibility is preliminarily assessed at prototype scale.
Abstract: This paper establishes a theoretical framework for vertical adaptive layer skipping, proving three foundational results: (i) an Expected FLOPs formula (theorem 2) giving a closed-form expression for the computational cost of arbitrary per-sample skip schedules as a function of layer-wise skip probabilities; (ii) function-space superset (theorem 10) and strict inclusion (theorem 11) theorems showing that skip-layer models are strictly contained in—yet meaningfully approximate—the full-layer function space, with an explicit separating example; and (iii) a structural duality between VALSE and Mixture-of-Experts architectures (proposition 6), positioning vertical depth-wise sparsity as the orthogonal counterpart to horizontal width-wise sparsity. Building on this theory, we propose VALSE (Vertical Adaptive Layer Skipping for Efficiency), a per-sample, non-contiguous layer skipping method: a lightweight difficulty estimator scores each input from the first few layers, and per-layer gates selectively skip redundant layers—including arbitrary middle layers while retaining deeper ones—so that only the necessary depth is activated for each input, whose feasibility is preliminarily assessed at prototype scale.
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